Question: Calculate the product below and give your answer in scientific notation. $ {\left(3.0\times 10^{3} \right) \times \left(5.0\times 10^{1} \right) =\ ?} $
Solution: Start by collecting the significands and exponents. $ ({3.0} \times {10^{3}}) \times ({5.0} \times {10^{1}}) = ({3.0} \times {5.0}) \times ({10^{3}} \times {10^{1}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {15.0} \times {10^{3 \,+\, 1}}$ $= {15.0} \times {10^{4}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${15.0}$ is the same as ${1.50 \times 10}$ or ${1.50 \times 10^{1}}$. $ = {1.50 \times 10^{1}} \times {10^{4}} $ $ = 1.50 \times 10^{{1} + {4}} $ $= 1.50\times 10^{5}$